I've been at warm ups where use of hands during up/down neck stretches was specifically discouraged since the feeling should be of lifting and stretching the long side toward the ceiling rather than compressing the short side toward the shoulder.

I've also been advised by a chiro that the forward/backward and side to side stretch are fine but that up/down is to be discouraged since it's not really in the normal range of motion for the cervical vertebrae, which makes sense if you think in terms of looking in different directions.